Find all the vectors so that...

Question

"Given the linear transformation F: $R^2$ to $R^2$, $F((x;y))=(2x;x)$ find all the vectors $v$ from $R^2$ so that $F(v)=2v$"

Can you help me? If I think the vector $v$ as $(v1;v2)$, the linear transformation tells me that the resulting vector would be $(2v1;v1)$, but after that what should I do?

Answer 1

$(2x,x)=(2x,2y)$ says that $x=2y$. So the answer is all vectors of the form $(2y,y)$ where $y$ is real number.